The BRUTE PSF-R algorithm estimates the characteristics length (r\(_0\) ) of the spatial power spectral density of the turbulence, fitting an analytical model onto the deformable mirror history and wavefront sensor data.
We used here a modal representation of the power spectral density (PSD) adapting the Noll (1976)[1]} formula, fitting the power law on the power spectral density of the modal description of pseudo open loop WF.
The point is to identify in that PSD the original atmospheric turbulence contribution, separating the effect of the noise.
We assumed that tip-tilt modes are dominated by the telescope vibrations, thus excluding these from the power law fit.
The fit allows extrapolating the modal amplitude of the uncontrolled components (the modes- or the frequencies higher than the one controlled by the SCAO system), finally estimating the orthogonal part of the wavefront.
